I thought this video from Every Frame a Painting was pretty interesting. It traces the development of how films/TV handle texting and the internet on screen.
For those of you too lazy to watch the video, it concludes that for texting, the best solution is simply showing text onscreen, with no speech bubbles or cutaways. It lets you keep watching the actors’ performances while inferring who is texting whom, which keeps the viewer engaged. This was first popularized in BBC’s Sherlock in 2010, but has been used a lot since then.
The video argues that nobody has yet come up with a good way to show internet usage, and that’s something that filmmakers still need to innovate on in order to find a solution.